On the slope of non-algebraic holomorphic foliations

Hong, Jie; Lu, Jun; Tan, Sheng-Li

doi:10.1090/proc/15097

On the slope of non-algebraic holomorphic foliations
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by Jie Hong, Jun Lu and Sheng-Li Tan PDF

Proc. Amer. Math. Soc. 148 (2020), 4817-4830 Request permission

Abstract:

Let $(Y, {\mathcal {G}})$ be a Riccati foliation on $Y$ and let $\pi :(X,{\mathcal {F}}){\rightarrow } (Y,{\mathcal {G}})$ be a double cover ramified over some normal-crossing curves. We will determine the minimal model of ${\mathcal {F}}$ and compute its Chern numbers $c_1^2({\mathcal {F}})$, $c_2({\mathcal {F}})$, and $\chi ({\mathcal {F}})=(c_1^2({\mathcal {F}})+ c_2({\mathcal {F}}))/12$. We will prove that the slope $\lambda ({\mathcal {F}})=c_1^2({\mathcal {F}})/\chi ({\mathcal {F}})$ satisfies $4\leq \lambda ({\mathcal {F}})<12$.

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